No, freedom is more important.

No, police should not be allowed to block data transmission whenever they like, because it is scary that the police would have that much power over the people. We do not have martial law in the United States. People should be able to communicate, even during times of social unrest. That would be too much police control.

No, transmission of information and ideas is key to preserving individual liberty against an authoritarian state

In this day and age, quick and easy transmission of information and media between people is one of the first and foremost ways to protect people from being abused by those with power over them. While it may be too late to save a person from being gunned down by a policeman in the street with little cause, it is not too late to send an outside account of the situation, including pictures or video perhaps, to friends, family, strangers, or the media. Such an act could bring justice to the family of the victim, punishment to the officer, and perhaps further repercussions for the police department, in the name of justice. Were authorities able to block this transmission, via confiscation of the devices used to send the information, or perhaps remotely with a blanket transmission blocking device of some sort (which I don't believe exists today, but is not beyond the realm of future possibilities), what method would there be to challenge the official police account? A citizen's word against a trained officer of the law is not always accepted as the more trustworthy of the two. So, in the interest of protecting citizens from their government, something which the United States was founded on, police should not be allowed to block data transmission whenever they choose.